Q. One litre of a gas is maintained at pressure 72 cm of mercury. It is compressed isothermally so that its volume becomes $900\ cm^{3}$. The value of stress and strain will be respectively
A) $0.106\ Nm^{- 2}\ and\ 0.1$
B) $1.106\ Nm^{- 2}\ and\ 0.1$
C) $106.62\ Nm^{- 2}\ and\ 0.1$
D) $10662.4\ Nm^{- 2}\ and\ 0.1$
Explanation
(d) According to Boyle’s law, $p_{2}V_{2} = p_{1}V_{1}$
Or ${\ p}_{2} = p_{1}\left( \frac{V_{1}}{V_{2}} \right)\ $
Or $p_{1} = 72\ \times 1000/900$=80 cm of Hg.
Stress = increase in pressure
= $p_{2} - p_{1} = 80 - 72 = 8\ $
= $1066.4\ \ Nm^{- 2}$
Volumetric strain = $\frac{V_{1} - \ V_{2}}{V_{1}} = \ \frac{1000 - 900}{1000} = 0.1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.